2021/08/01 by Ezequiel Barbosa, Allan Freitas, Barbosa, Ezequiel +5
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2108.00441
openalex publication_date 2021/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we investigate the existence of compact free-boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free-boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.